Cobordism category of plumbed 3-manifolds and intersection product structures
Geometric Topology
2009-01-27 v1 Algebraic Topology
Abstract
In this paper, we introduce a category of graded commutative rings with certain algebraic morphisms, to investigate the cobordism category of plumbed 3-manifolds. In particular, we define a non-associative distributive algebra that gives necessary conditions for an abstract morphism between the homologies of two plumbed 3-manifolds to be realized geometrically by a cobordism. Here we also consider the homology cobordism monoid, and give a necessary condition using w-invariants for the homology 3-spheres to belong to the inertia group associated to some homology 3-spheres.
Keywords
Cite
@article{arxiv.0901.3941,
title = {Cobordism category of plumbed 3-manifolds and intersection product structures},
author = {Yoshihiro Fukumoto},
journal= {arXiv preprint arXiv:0901.3941},
year = {2009}
}
Comments
25 pages